MGL-modules over a scheme are equivalent to motivic spectra with finite syntomic transfers, and the infinite P^1-loop space of MGL is the A^1-homotopy type of the moduli stack of finite syntomic schemes.
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Modules over algebraic cobordism
MGL-modules over a scheme are equivalent to motivic spectra with finite syntomic transfers, and the infinite P^1-loop space of MGL is the A^1-homotopy type of the moduli stack of finite syntomic schemes.